Effective dynamics of the hybrid quantization of the Gowdy T^3 universe

The quantum dynamics of the linearly polarized Gowdy T^3 model (compact inhomogeneous universes admitting linearly polarized gravitational waves) is analyzed within Loop Quantum Cosmology by means of an effective dynamics. The analysis, performed via analytical and numerical methods, proves that the behavior found in the evolution of vacuum (homogeneous) Bianchi I universes is preserved qualitatively also in the presence of inhomogeneities. More precisely, the initial singularity is replaced by a big bounce which joins deterministically two large classical universes. In addition, we show that the size of the universe at the bounce is at least of the same order of magnitude (roughly speaking) as the size of the corresponding homogeneous universe obtained in the absence of gravitational waves. In particular, a precise lower bound for the ratio of these two sizes is found. Finally, the comparison of the amplitudes of the gravitational wave modes in the distant future and past shows that, statistically (i.e., for large samples of universes), the difference in amplitude is enhanced for nearly homogeneous universes, whereas this difference vanishes in inhomogeneity dominated cases. The presented analysis constitutes the first systematic effective study of an inhomogeneous system within Loop Quantum Cosmology, and it proves the robustness of the results obtained for homogeneous cosmologies in this context.Comment: 21 pages, 11 figures, RevTex4-1 + BibTe

High-order gauge-invariant perturbations of a spherical spacetime

We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it is possible to construct the invariants

Conserved quantities in isotropic loop quantum cosmology

We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This quantity $Q$ relates the semi-classical limit of the wavefunction at large values of the spatial volume, but opposite triad orientations. Moreover, there is a similar quantity for generic difference equations of one parameter arising from a self-adjoint operator.Comment: 6 pages, to be published in Europhysics Letter

Big Bounce and inhomogeneities

The dynamics of an inhomogeneous universe is studied with the methods of Loop Quantum Cosmology as an example of the quantization of vacuum cosmological spacetimes containing gravitational waves (Gowdy spacetimes). The analysis performed at the effective level shows that: (i) The initial Big Bang singularity is replaced (as in the case of homogeneous cosmological models) by a Big Bounce, joining deterministically two large universes, (ii) the universe size at the bounce is at least of the same order of magnitude as that of the background homogeneous universe, (iii) for each gravitational wave mode, the difference in amplitude at very early and very late times has a vanishing statistical average when the bounce dynamics is strongly dominated by the inhomogeneities, whereas this average is positive when the dynamics is in a near-vacuum regime, so that statistically the inhomogeneities are amplified.Comment: RevTex4, 4 pages, 2 figure

Corrigendum to "Assessment of tsunami hazards for the Central American Pacific coast from southern Mexico to northern Peru" published in Nat. Hazards Earth Syst. Sci., 14, 1889–1903, 2014

No abstract available

Assessment of tsunami hazards for the Central American Pacific coast from southern Mexico to northern Peru

Abstract. Central America (CA), from Guatemala to Panama, has been struck by at least 52 tsunamis between 1539 and 2013, and in the extended region from Mexico to northern Peru (denoted as ECA, Extended Central America in this paper) the number of recorded tsunamis in the same time span is more than 100, most of which were triggered by earthquakes located in the Middle American Trench that runs parallel to the Pacific coast. The most severe event in the catalogue is the tsunami that occurred on 2 September 1992 off Nicaragua, with run-up measured in the range of 5–10 m in several places along the Nicaraguan coast. The aim of this paper is to assess the tsunami hazard on the Pacific coast of this extended region, and to this purpose a hybrid probabilistic-deterministic analysis is performed, that is adequate for tsunamis generated by earthquakes. More specifically, the probabilistic approach is used to compute the Gutenberg–Richter coefficients of the main seismic tsunamigenic zones of the area and to estimate the annual rate of occurrence of tsunamigenic earthquakes and their corresponding return period. The output of the probabilistic part of the method is taken as input by the deterministic part, which is applied to calculate the tsunami run-up distribution along the coast

Second and higher-order perturbations of a spherical spacetime

The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.Comment: Accepted for publication in Physical Review

The Euro-Mediterranean Tsunami Catalogue

A unified catalogue containing 290 tsunamis generated in the European and Mediterranean seas since 6150 B.C. to current days is presented. It is the result of a systematic and detailed review of all the regional cata- logues available in literature covering the study area, each of them hav- ing their own format and level of accuracy. The realization of a single catalogue covering a so wide area and involving several countries was a complex task that posed a series of challenges, being the standardization and the quality of the data the most demanding. A “reliability” value was used to rate equally the quality of the data for each event and this pa- rameter was assigned based on the trustworthiness of the information related to the generating cause, the tsunami description accuracy and also on the availability of coeval bibliographical sources. Following these cri- teria we included in the catalogue events whose reliability ranges from 0 (“very improbable tsunami”) to 4 (“definite tsunami”). About 900 docu- mentary sources, including historical documents, books, scientific reports, newspapers and previous catalogues, support the tsunami data and de- scriptions gathered in this catalogue. As a result, in the present paper a list of the 290 tsunamis with their main parameters is reported. The online version of the catalogue, available at http://roma2.rm.ingv.it/en/faci lities/data_bases/52/catalogue_of_the_euro-mediterranean_tsunamis, provides additional information such as detailed descriptions, pictures, etc. and the complete list of bibliographical sources. Most of the included events have a high reliability value (3= “probable” and 4= “definite”) which makes the Euro-Mediterranean Tsunami Catalogue an essential tool for the implementation of tsunami hazard and risk assessment

Mode coupling of Schwarzschild perturbations: Ringdown frequencies

Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity $(\ell=2,m=\pm 2)$ perturbations and odd-parity $(\ell=2,m=0)$ ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that ---in contrast to previous predictions in the literature--- the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects